1. Field of the Invention
The present invention is directed to a method for improving the signal-to-noise ratio in the operation of a nuclear magnetic resonance tomography apparatus, also known as a magnetic resonance imaging tomography apparatus, using the known echo planar imaging (EPI) method.
2. Description of the Prior Art
A method for operating a nuclear magnetic resonance tomography apparatus known as the echo planar imaging (EPI) method is disclosed in European application 0 076 054, corresponding to U.S. Pat. No. 4,509,015. In summary, the echo planar imaging method includes the generation of an RF excitation pulse which is made slice-selective by simultaneously generating a magnetic field gradient in a first direction. A phase coding gradient is generated in a second direction, and a read-out gradient consisting of a gradient pulse sequence changing in polarity from pulse-to-pulse is generated in a third direction. The nuclear magnetic resonance signal acquired under the read-out gradient is phase demodulated, and is conducted through a bandpass filter. The output of the filter is digitized at a sampling rate and for each gradient pulse, is written into a row of a raw data matrix in the k-space. An image matrix is derived from the raw data matrix by two-dimensional Fourier transformation, and an image is produced from the image matrix.
Further details of the echo planar imaging method are discussed below in connection with FIGS. 1-9 to assist in the explanation of a problem associated with that known method to which the improvement disclosed herein is directed.
The basic components of a conventional nuclear magnetic resonance tomography apparatus are shown in FIG. 1. Coils 1-4 generate a static, fundamental magnetic field in which, if the apparatus is used for medical diagnostics, the body of a patient 5 to be examined is situated. Gradient coils are provided for generating independent orthogonal magnetic field components in the x, y and z directions, according to the coordinate system 6. For clarity, only gradient coils 7 and 8 are shown in FIG. 1, which generate the x-gradient in combination with a pair of identical gradient coils disposed on the opposite side of the patient 5. Sets of y-gradient coils (not shown) are disposed parallel to the body 5 above and below the body 5, and sets of z-gradient coils (not shown) are disposed at the head and feet of the body 5 extending transversely relative to the longitudinal axis of the body 5.
The apparatus also includes an RF coil 9 which excites selected nuclei in the body 5 so that nuclear magnetic resonance signals are generated, and also serves to acquire the resulting nuclear magnetic resonance signals.
The coils 1, 2, 3, 4, 7, 8 and 9 bounded by a dot-dash line 9 represent the actual examination instrument. The instrument is operated by an electrical arrangement which includes a fundamental field coils supply 11 for operating the coils 1-4 and a gradient fields coils supply 12 for operating the gradient coils 7 and 8 and the further gradient coils.
Via a switch 19, the RF coil 9 can be connected to an RF transmitter 15, in an excitation mode, or to an amplifier 14 in a signal reception mode. The amplifier 14 and the transmitter 15 are a part of an RF unit 16, which is connected to a process control computer 17. The computer 17 is also connected to the gradient fields coils supply 12. The computer 17 constructs an image from the nuclear magnetic resonance signals, which is portrayed on a display 18.
A number of pulse sequences are known for operating the RF unit 16 and the gradient coils. Methods have prevailed wherein the image generation is based on a two-dimensional or a three-dimensional Fourier transformation. One such method is the aforementioned echo planar imaging method.
A pulse sequence used in the echo planar imaging method is shown in FIGS. 2-6. A radio-frequency excitation pulse RF, shown in FIG. 2, is generated which excites nuclei in a slice of the examination subject which is selected by a slice-selection gradient G.sub.Z in the z-direction, shown in FIG. 3, and generated simultaneously with the pulse RF. The direction of the gradient G.sub.Z is subsequently inverted, the negative gradient portion of G.sub.Z canceling the dephasing of the nuclear spins which was caused by the positive portion of the gradient G.sub.Z.
After excitation, a phase coding gradient G.sub.Y and a read-out gradient G.sub.X are generated. There are various possibilities for the respective curves of these two gradients. A phase coding gradient G.sub.Y is shown in FIG. 4 which remains continuously activated during the read-out phase. An alternative phase coding gradient G.sub.Y is shown in FIG. 5 which consists of individual pulses ("blips") which are activated upon the occurrence of each polarity change of the read-out gradient G.sub.X. The phase coding gradient is preceded by a dephasing in gradient G.sub.Y in the negative y-direction. The read-out gradient G.sub.X is activated with a constantly changing polarity, as a result of which the nuclear spins are alternately dephased and rephased, so that a sequence of signals S arises. After a single excitation, so many signals are required that the entire Fourier k-space is scanned, i.e., the existing information is adequate for the reconstruction of a complete tomogram. For this purpose, an extremely rapid switching of the read-out gradient G.sub.X with high amplitude is required, which cannot be achieved with square-wave pulses which are usually employed in NMR imaging. A standard solution to this problem is the operation of the gradient coil which generates the gradient G.sub.X in a resonant circuit, so that the gradient G.sub.X has a sinusoidal shape.
The nuclear magnetic resonant signals S which arise are sampled in the time domain, are digitized, and the numerical values acquired in this manner are entered into a measurement matrix for each read-out pulse. The measurement matrix can be viewed as a measured data space, and in the exemplary two-dimensional embodiment as a measured data plane, in which the signal values are measured on an equidistant network of points. This measured data space is usually referred to in nuclear magnetic resonant tomography as the k-space.
Data identifying the spatial derivation of the signal contributions, which is needed for image generation, is coded in the phase factors, with the relationship between the locus space (i.e., the image) and the k-space being mathematically representable by a two-dimensional Fourier transformation. Each point in the k-space (in this case the k-plane) is therefore representable by the relationship: ##EQU1## wherein .gamma. is the gyromagnetic ratio, and .zeta.(x,y) is the spin density distribution taking the relaxation times into consideration.
In FIGS. 8 and 9, the positions of the acquired measured values are schematically illustrated by points on a k-space (k-plane). FIG. 8 shows the case for the continuous gradient G.sub.y of FIG. 4, and FIG. 9 shows the case for the gradient G.sub.y shown in FIG. 5 in the form of a series of blips. For the Fourier transformation, the values must lie in an equidistant network of points, which is not the case in the examples shown in FIGS. 8 and 9. The acquired measured values therefore cannot be directly utilized, and an interpolation of the measured values onto an equidistant network of points must be undertaken.
The analog measured signal S is subjected to low-pass filtering to reduce the noise which arises in the signal acquisition. To optimize the signal-to-noise ratio, the bandwidth of the low-pass filter should exactly correspond to the signal bandwidth of the useful signal. The signal bandwidth .DELTA.f.sub.s is not constant given a gradient which is not constant, however, the acquisition bandwidth, and thus the noise bandwidth .DELTA.f.sub.r as well, by contrast, are constant given equidistant sampling of the nuclear magnetic resonance signal S at the chronological spacings .delta.t with .DELTA.f.sub.r =(.delta.t).sup.-1. The signal bandwidth for a sinusoidal read-out gradient is: ##EQU2## wherein G.sub.OX is the amplitude of the gradient G.sub.X and .omega..sub.G is the frequency of the gradient of G.sub.X.
The bandwidth of the phase coding gradient must also be taken into consideration. If the phase coding gradient G.sub.Y is maintained constant in accord with FIG. 4, the bandwidth is: ##EQU3##
In the case of chronologically equidistant sampling which satisfies the sampling theorem, i.e., sampling at an interval .gamma.t=T.sub.G /.pi.N, identical image windows in the x-direction and y-direction (.DELTA.x=.DELTA.y) and identical resolution in the x-direction and in the y-direction (N.sub.x and N.sub.y =N), ##EQU4## is the bandwidth of the nuclear magnetic resonant signal S. In the above expressions, T.sub.G is the period of the G.sub.Y, N.sub.x is the column number of the image matrix and N.sub.y is the row number of the image matrix.
The signal bandwidth is thus not constant during sampling, due to the sampling of the nuclear magnetic resonance signal S with a non-constant rate in the k-space. Heretofore, the bandwidth .DELTA.f.sub.s of the bandpass filter for the analog nuclear magnetic resonance signal (time domain signal) was defined such that the sampling theorem was just satisfied for the maximum sampling rate in the k-space, i.e. the bandwidth was defined as a constant having the value N.sup.2 .multidot.(.pi./4).multidot.T.sub.G for an image matrix of N.times.N picture elements. The bandwidth of the low-pass filter thus becomes unnecessarily large for the largest chronological portion of the scanning (or sampling. A large bandwidth, however, also means increased noise. Maintained a low signal-to-noise ratio, however, is an especially critical problem in the echo planar imaging method.